Analytical Chem istry - DePauw University

Chapter 7 Collecting and Preparing Samples297mR2 = K s7.5where K s is a sampling constant equal to the mass of a sample producing apercent relative standard deviation for sampling of ±1%. 8Example 7.7The following data were obtained in a preliminary determination of theamount of inorganic ash in a breakfast cereal.Mass of Cereal (g) 0.9956 0.9981 1.0036 0.9994 1.0067% w/w Ash 1.34 1.29 1.32 1.26 1.28What is the value of K s and what size samples are needed to give a percentrelative standard deviation for sampling of ±2.0%. Predict the percentrelative standard deviation and the absolute standard deviation if we collect5.00-g samples.Problem 8 in the end of chapter problemsasks you to derive equation 7.5.So l u t i o nTo determine the sampling constant, K s , we need to know the average massof the cereal samples and the relative standard deviation for the amount ofash. The average mass of the cereal samples is 1.0007 g. The average % w/wash and its absolute standard deviation are, respectively, 1.298% w/w and0.03194% w/w. The percent relative standard deviation, R, therefore, isssamp0. 03194%w/wR = × 100 = × 100 = 24 .6%X 1. 298%w/wSolving for K s gives its value as2 2K = mR = (. 1 0007 g)( 246 . ) = 6.06 gsTo obtain a percent relative standard deviation of ±2%, samples need tohave a mass of at leastm = K sR= 606 . g= 15 . g22(2.0)If we use 5.00-g samples, then the expected percent relative standard deviationisKs606 . gR = = = 110 . %m 5.00 gand the expected absolute standard deviation isssampRX (. 110)( 1. 298% w/w)= = = 0. 0143% w/w100 1008 Ingamells, C. O.; Switzer, P. Talanta 1973, 20, 547–568.